Max is an overloaded name; there are actually two
max functions.
template <class T> const T& max(const T& a, const T& b);
template <class T, class BinaryPredicate>
const T& max(const T& a, const T& b, BinaryPredicate comp);
Description
Max returns the greater of its two arguments; it returns the first
argument if neither is greater than the other.
The two versions of max differ in how they define whether one
element is less than another. The first version compares
objects using operator<, and the second compares objects using
the function objectcomp.